SOLUTION: find the altitude of an equilateral triangle if a side is 6 mm long

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Question 739049: find the altitude of an equilateral triangle if a side is 6 mm long
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
In an equilateral triangle all 3 sides are equal in length and angles are 60 degrees each

the altitude bisects the top angle and forms two equal right triangles within the original triangle
This means that you can use the fact that the sine of an angle is defined as the opposite side divided by the hypotenuse where the opposite side is the altitude and the hypotenuse is the known side
altitude%2Fside+=+sine%2860+%29
altitude+=+side%2Asine%2860+%29
sine%2860+%29+=+0.8660254 and side+=6mm
Therefore:
altitude+=+0.8660254%2A6mm
altitude+=+5.1961524mm

or, you can use Pythagorean theorem using right triangle formed by altitude (one leg), half of the side (other leg) and side (hypotenuse):
altitude%5E2+=%286+mm%29%5E2-%283mm%29%5E2
altitude%5E2+=36+mm%5E2-9+mm%5E2
altitude%5E2+=27mm%5E2
altitude+=sqrt%2827mm%5E2%29
altitude+=5.1961524mm